Libor Market Model

Abstract

This chapter introduces the LIBOR market model, which is the standard model for derivatives pricing. Because the topic of this book is risk management, we do not deal with the details of pricing. Instead, this chapter introduces the model, focusing on the implications of the real-world model.

First, we give a definition of the LIBOR market model, following Jamshidian (1997). Next, we define the LIBOR market model under the real-world measure (hereinafter, LMRW), and show, following the method of Yasuoka (2013b), that the model exists. Additionally we find the models under the spot LIBOR measure and under a forward measure that are implied by the LMRW.

Finally, we verify the numerical differences of the LIBOR process according to choice of measure. The study on the real-world model will be developed in Chapter 9.

Keywords: Arbitrage-free, Arbitrage pricing, BGM model, Change of num´eraire, Deterministic volatility, Forward LIBOR, Forward measure, HJM model, LIBOR market model, LIBOR volatility, LMRW, Lognormal distribution, Market price of risk, Martingale approach, Positive interest rate, Real-world measure, Risk-neutral model, Spot LIBOR measure, State price deflator, Terminal measure.